A universal set of gates is a set of gates which is necessary to generate all possible gates.
(Funktionale Menge basically ($\land, \lnot$))

![[Pasted image 20260806095829.png]]

## Pauli Gates

![[Pasted image 20260806095904.png]]

But we can't create all gates from only Pauli matrices.
For example, because we only manipulate a single qubit, we cant create the CNOT gate, which creates entanglement.
And we cannot create all single-qubit gates from only pauli matrices either... because the product of pauli matrices is always a pauli matrix again or the identity..


## Other Gates

![[Pasted image 20260806100803.png]]


## Rotation Gates

![[Pasted image 20260806100821.png]]![[Pasted image 20260806100826.png]]

## Clifford Gates

![[Pasted image 20260806100838.png]]


## Gottesmann-Knill theorem

![[Pasted image 20260806100859.png]]![[Pasted image 20260806100904.png]]
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